Question

Consider the following sample data

35 12 26 78 90 15 23 65

23 55 73 85 17 28 35 42

65 98 89 75 57 63 43 11

You want to create a confidence interval for this sample at the significance level of 95%. What is the standard error in your confidence interval calculation? What is the margin of errors in your confidence interval calculation? What is the degree of freedom in your confidence interval calculation?

Answer 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 50.125

S = 27.69447049

n = 24

df = n – 1 = 23

Confidence level = 95%

Critical t value = 2.0687

(by using t-table)

Standard error = S/sqrt(n)

Standard error =27.69447049/sqrt(24)

Standard error = 5.653110116

Margin of error = t*S/sqrt(n)

Margin of error = 2.0687*27.69447049/sqrt(24)

Margin of error = 2.0687*5.653110116

Margin of error = 11.6943

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 50.125 ± 2.0687*27.69447049/sqrt(24)

Confidence interval = 50.125 ± 2.0687*5.653110116

Confidence interval = 50.125 ± 11.6943

Lower limit = 50.125 - 11.6943 = 38.4307

Upper limit = 50.125 + 11.6943 = 61.8193

Confidence interval = (38.4307, 61.8193)